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How do you find the derivative of #g(x)=-5# using the limit process?

Answer 1

Emma Aldridge

Please see below.

#g'(x) = lim_(hrarr0)(g(x+h)-g(x))/h#

# = lim_(hrarr0)(-5-(-5))/h#

# = lim_(hrarr0)0/h = lim_(hrarr0)(0cancel(h))/cancel(h)#

# = 0#

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Answer 2

Axel Alvarez

To find the derivative of g(x) = -5 using the limit process, you apply the definition of the derivative:

[ g'(x) = \lim_{h \to 0} \frac{g(x + h) - g(x)}{h} ]

Substitute the given function g(x) = -5:

[ g'(x) = \lim_{h \to 0} \frac{-5 - (-5)}{h} ]

[ g'(x) = \lim_{h \to 0} \frac{0}{h} ]

[ g'(x) = \lim_{h \to 0} 0 ]

[ g'(x) = 0 ]

So, the derivative of g(x) = -5 is g'(x) = 0.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.